We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling, and the dot is modeled as an interacting resonant level onto which the bulk fermions can tunnel. We solve the Hamiltonian exactly and construct all eigenstates. We study both the zero- and finite-temperature properties of the system, in particular, we compute the exact dot occupation as a function of the dot energy in all parameter regimes. The system is seen to flow from weak to strong coupling for all values of the bulk interaction, with the flow characterized by a nonperturbative Kondo scale. We identify the critical exponents at the weak- and strong-coupling regimes.
Luttinger-liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter
K. We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine
K from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two
K's for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.